A range of vascular grafts are utilized within the medical arts fields, but often such grafts do not permit sufficient healing due to many reasons. In particular, small diameter conventional vascular grafts do not permit sufficient tissue ingrowth or transmural endothelialization that would allow for proper healing and satisfactory long-term outcomes. Larger bore grafts often are too stiff and do not have proper ingrowth of surrounding tissue. Various approaches have been attempted to overcome these deficiencies in the prior art, with relative lack of success. This invention is designed to provide solutions to these serious and long misunderstood problems.